Integrated methods for precision manufacturing of tissue engineering scaffolds

ABSTRACT

Methods for the development and integration of multiple apparatuses and methods for achieving administration of stem cell therapies include precision manufacturing of tissue scaffolds and/or bioreactor substrates. The nano/microscale fiber material extrusion typifying the electrospinning process is married with the fiber alignment and layering characteristic of an additive manufacturing process. The method generates porous fibrous 3-D meshes with precision controlled structures from biopolymer melts and solutions and gels, blends, and suspensions with and without cells. A method of tracking the migration histories and shapes of stem cells on scaffold surfaces relies on immunofluorescent imaging and automated algorithms based on machine learning. The combination of the precision manufacturing method and the method of cell tracking and cell shape statistics, along with understanding of the intimate relationship between the cell shape/phenotype and scaffold architecture leads to an integrated method for cultivating and harvesting cells having desired phenotypes.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Patent ApplicationSer. No. 62/545,527 filed Aug. 15, 2017, the entire disclosure of which,including the specification, drawings, Attachment A, and Attachment B,is incorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under Grant No.CMMI-MME-1554150 awarded by the National Science Foundation. Thegovernment has certain rights in the invention.

FIELD OF THE INVENTION

The invention disclosed herein relates to the fields of additivemanufacturing, tissue engineering, scaffold and bioreactor design andfabrication, regenerative medicine, stem cell expansion, stem celldifferentiation, stem cell population homogeneity and heterogeneity, andautomated image-based screening methods for the classification of stemcell phenotypes.

BACKGROUND OF THE INVENTION

The current understanding in stem cell expansion and differentiation,generally demonstrated on two-dimensional (“2-D”) substrates, is that itis necessary to change the stiffness of the substrate and/or include oneor more bioactive reagents (typically cocktails) so that the phenotypeof the stem cells can be conserved or modified during the expansion anddifferentiation of stem cells in regenerative therapies. Overall, theyields are relatively low and there are significant issues ofmaintaining the purity and homogeneity of the stem cell populations. Theknown methods for screening phenotypes of the stem cells (e.g., ELISA orflow cytometry) rely on bulk measurements and the use of relativelylarge stem cell populations. Thus, there are myriad issues in thecurrent state of regenerative medicine using stem cells.

SUMMARY OF THE INVENTION

Embodiments of the invention disclosed herein include one or moremethods that can be integrated to implement regenerative stem cell basedtherapies. The methods can be implemented under known paradigms, or maybe integrated to implement new paradigms or approaches to regenerativestem cell based therapies.

A first embodiment of the present invention includes a first method(“Method 1”) for precision manufacturing of three-dimensional (“3-D”)biomaterial scaffolds with precisely tunable porous microarchitecturesand geometrical feature sizes at the cell's operating length scales(10-100 μm). This dimensional scale window of precisely controllablemicroscale geometrical feature sizes is unattainable with other polymermelt based additive manufacturing technologies such as, for example,fused deposition modeling (widely known as “3-D printing”). Inembodiments of the method, high-fidelity fibrous scaffolds arefabricated through electrohydrodynamic (EHD) printing of a biopolymermelt using a melt electrowriting (“MEW”) technique. Embodiments of themethod are used to generate porous fibrous 3-D scaffolds withprecision-controlled porous microarchitectures from biopolymer melts. Inexactly the same way, embodiments of the method can be used to generate3-D scaffolds from a wide range of alternate materials such as polymersolutions, gels, blends and suspensions with and without cells. Inembodiments, the scaffolds are, or are component parts of, devices suchas static tissue engineered models and/or dynamic tissue engineeredmodels embedded within perfusable bioreactors.

A second embodiment of the present invention includes a second method(“Method 2”) for tailoring scaffold designs for stem cell expansion sothat the stem cell phenotype is not altered. Embodiments of the methodare used for homogeneous stem cell expansion without the presence of anycell-instructive chemicals and/or bioactive molecules and/or growthfactors.

A third embodiment of the present invention includes a third method(“Method 3”) for tailoring scaffold designs for stem cell expansion andsubsequent targeted differentiation of the stem cell phenotype.Embodiments of the method are used for homogeneous stem cell expansionand subsequent targeted differentiation without the presence of anycell-instructive chemicals and/or bioactive molecules and/or growthfactors.

A fourth embodiment of the present invention includes a fourth method(“Method 4”) for machine learning based classification of stem cellphenotypes using methods (e.g., immunofluorescent imaging) for tuningmanufacturing protocols for reproducible harvesting of targeted stemcell populations. This advanced manufacturing approach is biologicallyqualified with a metrology framework that models and classifies cellconfinement states under various substrate dimensionalities andarchitectures.

BRIEF DESCRIPTION OF FIGURES

The patent or application file contains at least one drawing executed incolor. Copies of this patent or patent application publication withcolor drawing(s) will be provided by the Office upon request and paymentof the necessary fee.

For a more complete understanding of the present invention, reference ismade to the following detailed description of an exemplary embodimentconsidered in conjunction with the accompanying figures, in which:

FIG. 1 is a schematic diagram presenting an overview of a conceptualintegration of Method 1, Method 2, Method 3, and Method 4 according toan embodiment of the present invention;

FIG. 2 is a schematic diagram illustrating a melt electrowritingapparatus according to an embodiment of the present invention;

FIGS. 3-7 are a set of reproductions of photographic images depictingthe polymer melt jet formed between the charged needle tip and thegrounded aluminum collector, the process regime known as free flowspinline regime, according to embodiments of the present invention;

FIG. 8 is a schematic diagram depicting a custom built manufacturingsystem, according to an embodiment of the present invention;

FIG. 9 is a screen-capture image of a thermogram and associated datadisplay depicting the custom built manufacturing system;

FIG. 10 is a reproduction of a photographic image of a portion of thecustom built manufacturing system;

FIG. 11 is a graph of the operating centigrade temperature of the custombuilt manufacturing system as a function of the distance between the tipand the collector;

FIG. 12 is a schematic illustrating the proposed heating element;

FIG. 13 is a schematic illustrating the key heat transfer mechanisms inthe polymer melt supply and free-flow regime;

FIGS. 14-18 are a set of reproductions of photographic images showingscaffolds fabricated from poly(caprolactone) (“PCL”) melts by a methodaccording to an embodiment of the present invention, the scaffoldshaving different configurations according to other embodiments of thepresent invention and the scaffolds of FIGS. 16, 17 and 18 specificallybeing woven scaffolds;

FIGS. 19-22 are a set of reproductions of photographic images, andrespective enlarged sub-figures (19A, 20A, 21A and 22A), showing fibrousscaffolds fabricated from PCL melts and a method according to anembodiment of the present invention, the scaffolds of FIGS. 19 and 20fabricated using conventional solution electrospinning technology, saidscaffolds having a non-woven configuration, and the scaffolds of FIGS.21 and 22 fabricated by a method according to an embodiment of thepresent invention and having a woven configuration with different porousmicroarchitectures. FIG. 21's Scaffold's configuration is designated asMEW|0-90° and that of scaffold D is designated as MEW|10-45°.

FIG. 23 is a schematic diagram of a petri dish;

FIGS. 24 and 25 are images showing attached neonatal human dermalfibroblasts' (NHDFs) shapes on a conventional flat culture substratewith cell shape control via tailoring of the porous microarchitecture ofthe scaffolds according to embodiments of the present invention;

FIGS. 26-28 are schematic diagrams of cells on the MEW|0-90° scaffoldwith accompanying micrographs (26A, 27A, 28A and 28B), with cell shapecontrol via tailoring of the porous microarchitecture of the scaffoldsaccording to embodiments of the present invention;

FIGS. 29 and 30 are schematic diagrams of cells on the MEW|0-45°scaffold with accompanying micrographs (29A, 29B, 30A and 30B), withcell shape control via tailoring of the porous microarchitecture of thescaffolds all according to embodiments of the present invention;

FIGS. 31-38 are multiple sets of photographic immunofluorescence imagesillustrating the expansion of stem cells using conventional expansionmethods employing flat surfaces, wherein FIGS. 31 and 32 show positivemarker expression, FIGS. 35 and 36 show no negative marker expressionafter 1 day of culture, FIGS. 33 and 34 show positive marker expressionand FIGS. 37 and 38 show negative marker expression after 7 days ofculture, the photographic images illustrating that stem cells lose theircharacteristic phenotype within one week of culturing, thussignificantly decreasing their expansion potential and introducingproblems with control of the purity and homogeneity of the stem cellpopulation;

FIGS. 39-50 are multiple sets of photographic immunofluorescence imagesFIGS. 39, 40 and 42 showing positive marker expression and FIGS. 41 and43 showing no negative marker expression) illustrating the expansion ofstem cells on scaffolds having porous microarchitectures realizedaccording to a method of the present invention, and the novel andunexpected finding that, under such scaffold geometries andarchitectures, stem cells conserve their phenotypes after 7 days ofculture, which cannot be achieved with conventional substrates, theexample of FIGS. 39-50 being the conservation of the stem cell phenotypefor at least one week on the MEW|0-90° scaffold, whereas with the PCLflat surfaces of the embodiment of FIGS. 31-38, the phenotype of thestem cells is altered within one week, thus significantly reducing thepotential for stem cell expansion;

FIGS. 51-62 are multiple sets of photographic immunofluorescence images(FIGS. 51-53 showing positive marker expression and FIGS. 54 and 55showing no negative marker expression) illustrating the expansion ofstem cells on scaffolds having porous microarchitecture realizedaccording to a method of the present invention, and the novel andunexpected finding that, under such scaffold geometries andarchitectures, stem cells conserve their phenotypes after 14 days ofculture, which cannot be achieved with conventional substrates, theexample of FIGS. 51-62 being the conservation of the stem cell phenotypefor at least one week on the MEW|0-90° scaffold, whereas with the PCLflat surfaces of the embodiment of FIGS. 31-38, the phenotype of thestem cells is altered within one week, thus significantly reducing thepotential for stem cell expansion;

FIGS. 63-74 are multiple sets of immunofluorescence photographic images(FIGS. 63-66 showing positive marker expression and FIGS. 67-70 showingno negative marker expression) further illustrating the expansion ofstem cells on scaffolds having porous microarchitectures realizedaccording to a method of the present invention, and the novel andunexpected finding that, under such scaffold geometries andarchitectures (e.g., the MEW|0-45° of FIG. 22), stem cells preservetheir phenotype for the first week of expansion, while the phenotype isconverted in a predictable manner into a new phenotype thereafter,showing that understanding the relationships between the geometries ofthe scaffolds and the differentiation route of the stem cells willgenerate a new method that will enable the harvesting of cellpopulations with targeted phenotypes based on the geometry of thescaffold alone;

FIGS. 75-82 are multiple sets of immunofluorescence photographic images(FIGS. 75 and 76 showing positive adipocyte expression and FIGS. 77 and78 showing bone differentiation marker expression, both 33 days afterculture on conventional flat substrates, and FIGS. 79-82) showing onlyadipocyte differentiation marker expression on MEW scaffolds) furtherillustrating the expansion of stem cells on scaffolds having porousmicroarchitectures realized according to a method of the presentinvention promoting homogeneous expansion and differentiation of stemcells;

FIG. 83 is a schematic diagram providing an overview of a cellclassification method according to an embodiment of the presentinvention;

FIG. 84 is a flow diagram of a feature extraction algorithm inaccordance with an embodiment of the present invention;

FIGS. 85-88 are a group of reproductions of photographicimmunofluorescence images showing cellular structures observed duringstem cell expansion according to a method of the present invention,wherein image FIG. 85 further is a colorized multi-channel maximumprojection image obtained by combining three different single channelmaximum projections, the single channel maximum projections obtained byprocessing Z-stack raw images, wherein the red channel is associatedwith the cytoskeleton, the blue channel is associated with the nucleus,and the green channel is associated with vinculin. FIG. 86 is agrayscale maximum projection of the red channel cell body image overlaidwith the contour of the segmented cell body, FIG. 87 is a grayscalemaximum projection of the blue channel image overlaid with the contourof the segmented nucleus, and FIG. 88 is a grayscale maximum projectionof the green channel image overlaid with the contour of the segmentedfocal adhesions (scale bar: 20 μm);

FIGS. 89-97 are a group of graphical illustrations of examples of afeature extraction procedure using single-cell automated bioimageanalysis of immunofluorescent images according to a method of thepresent invention, providing a demonstration of the performance of anautomated image processing algorithmic workflow according to anembodiment of the present invention that uses a representative cellcultured in 3-D microscale fibrous scaffold. FIGS. 89-97 illustrate analgorithmic procedure according to an embodiment of the presentinvention that allows the development of critical cellular andsubcellular focal adhesion morphometric and distribution metrics thatare useful for the training and application of the developedclassification method to various cell types according to an embodimentof the present invention;

FIGS. 98-103 present graphical examples (FIGS. 98, 100 and 102) andconfusion matrices (FIGS. 99, 101 and 103) illustrating the use of theclassification methodology according to embodiments of the presentinvention to different scaffold geometries, and the confinement statesof stem cells within the scaffolds during expansion, the graphicalexamples and confusion matrices documenting changes in cellular andsubcellular adhesion proteins for the different geometries (for allcells under analysis>100), and demonstrating that the novel 3-Dsubstrate architectures according to embodiments of the presentinvention induce uniform and geometry-dependent cell shapes andresulting phenotypes while, in contrast, the control stem cell cultureson flat surfaces or non-woven 2-D meshes with randomly oriented fibersinduce heterogeneous cell shapes, presumably inducing phenotypeheterogeneities; and

FIG. 104 is a schematic diagram of a concept for industrial exploitationof the classification method according to an embodiment of the presentinvention, further including feedback and feedforward controlmethodologies for the programmable expansion and harvesting of stemcells having phenotypes that are targeted and realized according to amethod of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Previously-known stem cell based therapies rely on the harvesting ofstem cells from the patient, followed by expansion of the cell number ina bioreactor system. Typically, this is achieved in conjunction withsubsequent direct and localized delivery (e.g., injection or infusion)of stem cell suspensions through various access routes that home to thesite of tissue injury. An alternative mode of stem cell delivery forenhanced cell engraftment and survival entails seeding the expanded stemcells on bioresorbable scaffolds with subsequent implantation of thetissue constructs to the targeted site of tissue injury. Prior to theinvention of the methods and structures disclosed herein and furtherembodiments thereof, there has been no extant sophistication of thedesign criteria for the bioreactor substrate and scaffold geometriesneeded to achieve high expansion rates while conserving theundifferentiated state of the stem cells (e.g., original phenotype or“sternness”), or of achieving a particular terminal differentiationstate (e.g., tissue-specific function) of the stem cells. Conserving thefunctional homogeneity of the stem cell population (i.e., avoidingfunctional heterogeneity of the population) to be administered into thebody of the patient is another issue resolved by embodiments of thepresent invention.

Embodiments of the present invention provide new methodologies forimproving the homogeneity during stem cell expansion, long-term in vitrodifferentiation, and phenotype screening and targeting in ways thatprovide novel and unexpected results. The elements of the invention arefirst instructed by the discoveries disclosed herein that demonstrate anintimate relationship between the geometry of the engineered bioreactoror scaffold and the manner in which stem cells expand and differentiate.It is disclosed that stem cells seeded on 3-D substrates generatedifferent types and distributions of stem cell shapes and phenotypes incomparison to their 2-D surface counterparts. Furthermore, it isdisclosed herein that the particular 3-D pore geometry has a profoundeffect on stem cell shape and the associated stem cell differentiationstates. For instance, normal human dermal fibroblasts (NHDFs) were grownon 3-D MEW scaffolds with 0-90° architecture (MEW|10-90°) scaffolds andon 3-D MEW scaffolds with 0-45° architecture (MEW|0-45°) scaffolds.Compared to a 2-D petri dish control, both scaffolds demonstrate moreuniform cell shapes. The former scaffold confined the cells in atwo-dimensional space, while the latter scaffold put them in a 3-Dconfined and suspended state. Motivated by this, stem cells that behavemorphologically similarly to NHDFs were cultured on 3-D MEW fibrousscaffolds demonstrating preservation of their stem cell phenotypesignificantly longer compared to 2-D conventional flat culturesubstrates.

As disclosed herein, a new manufacturing method according to anembodiment of the present invention allows precise control of the porousmicroarchitecture of a 3-D scaffold with cellular-relevant geometricalfeature sizes, providing control of the shapes and the phenotypes of theexpanded stem cells. Embodiments of the present invention include amethod to generate the desired types of scaffold geometry in areproducible and industrially scalable manner. Such embodiments of thepresent invention combine melt electrospinning and additivemanufacturing. Embodiments of this manufacturing method (designatedhereinafter as “the TCK method”) are used to fabricate scaffold meshesof geometrical fidelity and precision not encountered previously.Embodiments of the TCK method are used to fabricate novel scaffolddesigns involving, for example, 0-90 and 0-45 degree fibrousarchitectures with consistent fiber diameters, orientations, alignment,and interconnectivities.

The TCK method utilizes Melt Electrospinning Writing (MEW) tomanufacture the integrated scaffolds. In one embodiment,Poly(e-polycaprolactone) (PCL) is selected for MEW on the basis of itsFood and Drug Administration approval for in vivo applications,biocompatibility, long-term biodegradability, and relatively low andwide melt processing temperature window (60°-90° C.). PCL materialspecifications with an average molecular weight of 45,600 g/mol andpolydispersity of 1.219 can be used. Such can be obtained, for example,from Perstorp Ltd. of Warrington, UK (Capa6500).

PCL pellets are molded into 8 mm and 25 mm circular disks using aluminumshims between Teflon surfaces and a Carver press at 120° C. forsubsequent rheological characterization. This can be accomplished withthe advanced rheological extended system (ARES) of Rheometric Scientific(currently TA Instruments) in conjunction with stainless-steel paralleldisk fixtures with 25 mm diameter for small-amplitude oscillatory shear(SAOS) and steady torsional flow experiments. The force-rebalancetransducer of the rheometer is capable of measuring simultaneously boththe normal force and the torque. The oven temperature of the rheometeris controlled within ±0.1° C. The rheological characterizationexperiments can be carried out at 70° C., 80° C., and 90° C. and using aconstant 1 mm gap.

A high-resolution heat-assisted MEW system configuration can beestablished. The process design is guided by detailed characterizationof the thermorheological processing properties of the biomaterialsubstrate along with the fluid dynamics, heat transfer, andelectrostatics multiphysics phenomena governing the process underinvestigation. The overall system configuration is analyzed based onthree defined discrete process regimes.

First, the polymer melt supply regime can be composed of a glassLuer-lock 5 ml syringe (such is available for purchase from Hamilton,Reno, Nev.) and a stainless-steel needle tip with a plastic hub (such asthat obtainable from McMaster Carr, Elmhurst, Ill.) attached to it. Thepolymer melt can be maintained in a uniform melt state using anindustrial heat gun (e.g., Steinel, HG 2510 ESD). In addition, aprogrammable syringe pump (such as that obtained from Harvard Apparatus,Holliston, Mass.) is mounted vertically and used to set the volumetricflow rate by adjusting the speed of the plunger within a syringe (flowaccuracy being within 0.25% and reproducibility being within 0.05%). Thetemperature can be monitored both at the syringe barrel and thecapillary tip with an infrared FLIR thermal camera (such as the PM 290,Inframetrics, Thermacam). In the free-flow regime, a high-voltage source(a suitable source can be acquired from Gamma High Voltage Research,Ormond Beach, Fla.) is used for the application of a voltage potentialbetween the needle tip and a grounded electrically conductive collector.An aluminum collector is mounted on an x-y programmable stage (such asthat obtainable from ASI Applied Scientific Instrumentation, Eugene,Oreg.) that is sequentially mounted on a lab jack (obtained, e.g., fromNewport Corporation, Irvine, Calif.) (See FIGS. 8-13). The distancebetween the tip and the collector plate can be monitored using avertical digital meter (FIGS. 8-13) and set manually using the labjack's turning knob with a vertical positioning resolution of 0.5 mm. Tocompensate for ambient conditions that might affect the process, theoverall system configuration is placed on an antivibrating optical tablewith the spinning apparatus contained within a plexiglass enclosure.Furthermore, the temperature and humidity values within the enclosurecan be monitored using a multimeter (such as that which can be acquiredfrom Extech Instruments, Waltham, Mass.) equipped with a type Kthermocouple.

The heating element is composed of an industrial heat gun (HG) withcontrollable air flow (QHG) (0.002-0.008 m³/s) and adjustable airtemperature (THG) settings (49°-649° C.). The heat gun is mounted at theentrance of a heating tunnel housed by a transparent chamber constructedout of poly (methyl methacrylate) (FIG. 12). The syringe passes throughthe heating tunnel, and a small portion of the syringe needle tipreaches the interior of the chamber through an electrically conductivetape covering a circular opening created at the ceiling of the chamber.Heating insulation tapes are applied onto the back wall and the floor ofthe heating tunnel in order to minimize heat losses. The area of thecircular opening covered by the tape is kept tightly sealed in order toavoid disturbances along the spinline regime from the hot stream air.

The surface of the syringe is heated due to heat transfer via forcedconvection generated by the heat gun, and the ambient temperatureconditions along the spinline are governed by free convection through tothe heated tape. The heat transfer conditions are calibrated so that thetemperature at the surface of the syringe hosting the PCL melt ismaintained as the desired temperature. For example, it is determinedthat for the air flow rate of Q_(HG)=0.0017 m³/s and air temperature ofT_(HG)=132° C., the temperature on the syringe surface (Ts) is set andmaintained at 78±1° C. (FIG. 9). Thermal imaging using the FLIR cameraconfirms that the temperature at the surface of the syringe does notvary outside of the Ts±1° C. over the time course.

Thermocouple measurements along the spinline coordinate z (FIG. 10),where z=0 mm is considered a measurement point under the tip (Tt=40±5°C.) and z=30 mm is considered a measurement point on the surface of thecollector plate (Tc=30±5° C.), demonstrate the presence of anexponentially decaying temperature profile (FIG. 11). Due to the highthermal conductivity of glass and the small volume of polymer melthosted in the syringe barrel, it is assumed that the temperature of thepolymer melt (T_(o)) becomes equal to T_(s), and the system reachesthermal equilibrium after 1 h. The latter is also confirmed by measuringa stable spinline temperature profile regularly after the heat gun isset over the time course of 2 h. In this way, the presence oftemperature gradients higher than 5° C. along the process regimes thatmay yield variations in the temperature-dependent polymer viscosity, andthus in the flow field along the process regimes, are avoided.

Although studies that have used heated air systems have reported thatthe temperature at the spinneret may be difficult to control accuratelyusing this approach, the present study demonstrates that a heat-gunbased system is capable of maintaining uniform heating within thematerial head and a spinline temperature profile, whose higher end canbe set close to the onset crystallization temperature of PCL. Thiscapability can offer an alternative way of printing aligned fibers withsubmicron diameter by tuning the spinline temperature so as to induceprolonged stretching, through delayed “in-flight” fiber solidification.

Prior to the printing, pure PCL pellets are loaded into a glass syringe(Hamilton). Then, the syringe is placed in a laboratory convective ovenand heated for 24 h to remove any bubbles that may affect the processstability and downstream structural formability of the melt electrospunfibers. After assuring the homogeneity of the polymer melt, a needle tipat a prescribed nominal inner diameter (21 gauge—0.514 mm) is adaptedonto the syringe. The syringe with the attached tip is then placed inthe material head of the system, which is preheated at a temperature(T_(surf)=77.8° C.) with the heating element. At least 1 h is given tothe system prior to initiating the printing studies in order to reachthermal equilibrium.

Thin glass coverslips are taped on the grounded aluminum plate and usedas collectors for all the printing tasks. In this way, the structuralformability in terms of diameter and quality of the MEW fibers can becharacterized using bright field microscopy. An inverted motorizedmicroscope (such as the IX83 from Olympus in Tokyo, Japan) along withimage processing software (CELLSENS 2.11) can be used to image andcharacterize all samples. The fiber diameter can be measured directlyfrom the acquired images at five different points along the length ofeach fiber for statistical significance, and an average fiber diameteralong with its standard deviation can be recorded. The apparent poresize is determined as the average value of the circle diameters thatcould be fitted inside each scaffold pore. All measurements are doneusing a 20× objective lens with the magnification set at 12.6.

The identification of relevant dimensionless groups can be carried outusing a classical dimensional analysis technique starting with processand system-specific independent parameters. The following definitionsare employed. “n” is the number of independent variables relevant to theprocess. “j” is the number of base dimensions found in the n variables.“j” is the number of variables necessary to be consideredsimultaneously. “k” is the number of the independent Π terms that can beidentified to describe the process and is equal to n−j (k=n−j).

The total number of independent variables, n, is equal to 12. Table 1enumerates these variables and their base dimensions, where M stands formass (SI unit: kilogram), L stands for length (SI unit: meter), T fortime (SI unit: second), Θ for temperature (SI unit: Kelvin), and A forelectric current (SI unit: Ampere).

TABLE 1 List of independent variables along with base dimensions: j ={L, M, T, A, Θ} Variables R_(o) d Q V_(p) T_(t) T_(o) ρ η ε γ λ g SIunits m m m³/s V K K kg/m³ Pa · s $\frac{F}{m}$ $\frac{N}{m}$ s kg/m³Equivalent — — — kg m²s⁻³A⁻¹ — — — m kg s⁻¹ s⁴A²kg⁻¹m⁻³ kg s⁻² — — withmore basic SI units Base L L L³T⁻¹ ML²T⁻³A⁻¹ Θ Θ ML⁻³ L⁻¹MT⁻¹ T⁴A²M⁻¹L⁻³MT⁻² T LT⁻² dimensionsThis number of base dimensions is equal to 5 with j′={L, M, T, A, Θ}.Next, j is determined by assuming that j=j′ and scanning for j repeatingvariables which do not form a dimensionless product. The prescribednumber of five independent variables leads to the following independentvariables j={d, Q, V_(p), T_(t), γ}. Thus, the number of independentdimensionless Π terms that could be formed would be equal tok=n−j=12−5=7. The following step consists of the Π_(i), i=1, 2, 7 termformation. Each term is formed by forming a power product of the jrepeating variables with the additional variable.

The procedure followed for P1 term formation is shown:Π₁ =R _(o) ^(a) ¹ g ^(a) ² ε^(a) ³ T _(t) ^(a) ⁴ γ^(a) ⁵ η_(p) ⁻¹  (1)Then, the dimensions of the various quantities are inserted inside Eq.(1)dimension of Π₁ =L ^(a) ¹ ^(+a) ² ^(−3a) ³ M ^(−a) ³ ^(+a) ⁵ ⁻¹ T ^(−2a)² ^(+4a) ³ ^(−2a) ⁵ ⁺¹ A ^(2a) ³ Θ^(a) ⁴   (2)To obtain a dimensionless parameter Π, each exponent M, L, T, etc., toneeded vanish, thereby yielding a system of linear algebraic equationsa ₁ +a ₂−3a ₃=0  (3)−a ₃ +a ₅=1  (4)−2a ₂+4a ₃−2a ₅=−1  (5)2a ₃=0  (6)a ₄=0  (7)

TABLE 2 List of dimensionless Π_(i), i = 1, 2 . . . , 7 terms Π₁ Π₂ Π₃Π₄ Π₅ Π₆ Π₇ $\frac{d^{1/2}\gamma}{g^{1/2}\eta_{p}}$$\frac{T_{t}}{T_{c}}$ $\frac{R_{o}}{d}$ $\frac{d^{5/2}g^{1/2}}{Q}$$\frac{g\; ɛ^{1/2}V_{p}}{d^{3/2}\gamma^{3/2}}$$\frac{d^{1/2}}{g^{1/2}\lambda}$ $\frac{\gamma}{d^{2}{dp}}$The solution of the system (Eqs. (3)-(7)) and its subsequentsubstitution in Eq. (1) yields a dimensionless term Π_(i) shown in Table2. The same procedure is followed for the formation of the remainingΠ_(i) terms shown in Table 2. Thus, the product combination of the Π_(i)dimensionless terms can lead to a single dimensionless number ΠΠ=Π₁*Π₂* . . . *Π₇  (8)Substituting for each individual Pi term from Table 2 yields thefollowing dimensionless H number, denoted as N₁ herein:

$\begin{matrix}{N_{1} = {\frac{y^{1/2}ɛ^{1/2}}{g^{1/2}}\frac{T_{t}}{\lambda\;\rho}\frac{R_{o}}{Tc}\frac{V_{p}}{{dQn}_{p}}}} & (9)\end{matrix}$To account for the translational stage speed U_(T) as an independentparameter, an additional dimensionless group Π_(s) is formulated as anadditional multiplier in Eq. (8)

$\begin{matrix}{\Pi_{8} = \frac{U_{T}}{R_{o}^{1/2}g^{1/2}}} & (10)\end{matrix}$yielding the following N₂ term:

$\begin{matrix}{N_{2} = {\frac{y^{1/2}ɛ^{1/2}R_{o}^{1/2}}{g\;\lambda\;\rho}\frac{T_{t}}{T_{C}}\frac{V_{p}U_{T}}{{dQn}_{p}}}} & (11)\end{matrix}$The formulation and calculation of two separate terms, N₁ and N₂, inturn enable the investigation of printability when the process isperformed under a stationary (U_(T)=0) and a moving collector (U_(T)>0),respectively. In the former case, the N₁ term is a function of theindependent process parameters that govern the polymer melt jetformation in the free-flow regime. In the latter case, the N₂ termadditionally accounts for the translational stage speed (U_(T)), aprocess variable that quantitatively affects the fiber topography on thereceiving substrate. To be sure, the initial N₁ term is defined for thepreliminary procedural step of identifying the equilibrium stateconditions in the free-flow regime to ensure stable jet formation. Inthe absence of this preliminary step, the direct application of N₂ for astationary collector would yield a trivial printability value of zero.

What follows is a set of nondimensionalized equations that enable theidentification of the important dimensionless groups that need to betuned toward efficient printability.

A thin filament approximation is used, and by focusing on a small partof the melt electrospun stable jet region, a one-dimensional momentumbalance is made by considering the various forces affecting the jetprofile. The jet is subjected to: (a) Coulombic electrostatic, viscous,elastic, surface tension, and gravitational forces. Assuming axisymmetryalong the path from the tip of the spinneret up to the surface of thecollector (at distance, d) and using the characteristic quantitiesdefined in Table 3, the dynamics of the melt electrospun jet can bemodeled using the following system of nondimensional equations, where Ris the jet radius divided by the characteristic jet radius R_(o) justoutside of the needle tip, v is the jet velocity divided by thecharacteristic velocity v_(o), R is the jet radius, and the primeindicates derivatives with respect to the spinline coordinate z:

A(1) Conservation of Mass—Continuity:R ² v=1

A(2) Conservation of Momentum:

${Revv}^{\prime} = {{Bo} + {3( {1 - r_{n}} )\frac{( {R^{2}v^{\prime}} )^{\prime}}{R^{2}}} + \frac{T_{p}^{\prime}}{R^{2}} + {{Ca}\frac{R^{\prime}}{R^{2}}} + {E_{p}( {{\sigma\sigma}^{\prime} + {\beta\;{EE}^{\prime}} + \frac{2\; E\;\sigma}{R}} )}}$where Re, Bo, Ca, and E_(p) are defined in Table 3.

A(3) Conservation of Charge:σ=R

A(4) Electric Field:

$E_{t} = \frac{1}{( {1 + {2\; z} - {z^{2}/\chi}} )\sqrt{1 + ( R^{\prime} )^{2}}}$The viscoelastic nature of the polymer melt is taken into considerationby the use of the Giesekus model, which expresses the viscous polymerstress τ_(p) in terms of the applied deformation, which is representedby the strain rate tensor {dot over (γ)}

$\begin{matrix}{{\tau_{p} + {\lambda\;\tau_{p{(1)}}} - {\alpha\frac{\lambda}{n_{p}}\{ {\tau_{p} \cdot \tau_{p}} \}}} = {{- n_{p}}\overset{.}{\gamma}}} & {{A(5)}\;}\end{matrix}$The viscous polymer stress τ_(p) denotes the elastic nature of thematerial due to normal stresses that arise during its deformation, andthe strain rate tensor {dot over (γ)} is given by the sum of thevelocity gradient and its reciprocal. The input parameters of theGiesekus model that are determined by fitting the experimental raw dataon the basis of the corresponding rheological material functions foreach type of tested viscometric flow are the following: n_(p) representsthe polymer viscosity parameter, λ the relaxation time, and α themobility factor, which is a parameter related to the anisotropicBrownian motion and/or hydrodynamic drag on the constituent polymermolecules.

The nondimensional components of the viscous polymer stress tensor τ_(p)are given based on the constitutive Giesekus model (Eq. (1)) inaxisymmetric cylindrical coordinates as

$\begin{matrix}{{\tau_{p,{rr}} + {{De}( {{v\;\tau_{p,{rr}}^{\prime}} + {v^{\prime}\tau_{p,{rr}}}} )} + {\alpha\frac{De}{r_{n}}\tau_{p,{rr}}^{2}}} = {{- r_{n}}v^{\prime}}} & {A(6)} \\{{\tau_{p,{zz}} + {{De}( {{v\;\tau_{p,{zz}}^{\prime}} - {2v^{\prime}\tau_{p,{zz}}}} )} + {\alpha\frac{De}{r_{n}}\tau_{p,{zz}}^{2}}} = {{- 2}r_{n}v^{\prime}}} & {A(7)}\end{matrix}$

These dimensionless numbers calculated using the above equations arefurther summarized in Table 3 below.

TABLE 3 Characteristic quantities along with nondimensional numbersobtained based on the governing equations Characteristic quantitiesLength R_(o) Velocity $v_{o} = \frac{Q}{\pi\; R_{o}^{2}}$ Electric Field$E_{o} = {{E(0)} = \frac{2V_{p}}{R_{o}{\ln( {1 + {4{d/R_{o}}}} )}}}$Dimensionless groups and their definitions Bond number${Bo} = \frac{\rho\;{gR}_{o}^{2}}{{\eta_{o}( T_{m} )}v_{o}}$$( \frac{gravity}{inertia} )$ Electrostatic force parameter$E_{p} = \frac{ɛ_{o}E_{o}^{2}R_{o}}{{\eta_{o}( T_{m} )}v_{o}}$$( \frac{electrostatic}{inertia} )$ Capillary number${Ca} = \frac{{\eta_{o}( T_{m} )}v_{o}}{\gamma}$$( \frac{inertia}{{surface}\mspace{14mu}{tension}} )$Reynolds number${Re} = \frac{\rho\; v_{o}R_{o}}{\eta_{o}( T_{m} )}$$( \frac{inertia}{viscous} )$ Deborah number${De} = \frac{\lambda\; v_{o}}{R_{o}}$$( \frac{{relaxation}\mspace{14mu}{time}}{{time}\mspace{14mu}{scale}\mspace{14mu}{of}\mspace{14mu}{flow}} )$

Initiation of the printing process requires: (a) droplet emergence, (b)successful Taylor cone formation, and (c) subsequent emergence of acharged jet, which is electrostatically drawn across the spinlinecoordinate in the free-flow regime. All phenomena are dependent on therelative importance of the forces applied at the polymer melt jet.

Downstream pulling forces such as the gravitational and theelectrostatic Coulombic forces are related to the Bond (Bo) number andthe electrostatic force parameter (E_(p)), respectively. Upstreamresistive forces such as the viscous, the elastic, and the surfacetension forces are related to the Reynolds (Re) number, the Deborah (De)number, and the Capillary (Ca) number. According to the electrospinningoperating principle, Taylor cone formation occurs when the electrostaticforces overcome the capillary forces. Jet initiation and theelectrostatic drawing of the polymer melt jet are strongly dependent onthe viscoelasticity of the polymer melt. If the gravitational forces,along with the electrostatic drawing forces caused by the accumulationof the charges at the jet-ambient air interface, overcome the viscousand elastic stresses that are applied to the polymer melt, jetinitiation occurs. Thus, the proposed Printability Number should assumevalues within a domain defined by a set of independent material,process, and geometry-related parameters for which the printing processcan be realized.

A new dimensional analysis is employed based on measurable polymerproperties and controllable process parameters. Consistent with standardengineering practice, simplified dimensionless numbers are derived bytaking the product of the formulated ones. Specifically, sevendimensionless groups are formulated (Π_(1,2 . . . 7)) based on theprocedure detailed above. To this end, the N₁ number given by Eq. (9) isdefined as the Printability Number for a stationary collector anddenoted as N_(PR,1)

$\begin{matrix}{N_{{PR},1} = {\frac{\gamma^{1/2}ɛ^{1/2}}{g^{1/2}\lambda\;\rho}\frac{T_{t}}{T_{C}}\frac{R_{o}}{d}\frac{V_{p}}{Q\;{\eta_{p}( T_{m} )}}}} & (12)\end{matrix}$where η_(ρ)(T_(m)) denotes the melting temperature dependency of thepolymer viscosity, and the characteristic jet radius just outside theneedle tip, R_(o), is assumed to be equal to the needle tip diameter.

Material functions of the Giesekus model are used for nonlinear fittingof the experimental data and the determination of model-specific inputparameters for the polymer melt to be processed. As shown, the values ofthe loss modulus, G″, i.e., the energy dissipated as heat, are higherthan the values of the storage modulus, G′, i.e., the energy stored aselastic energy, over a broad range of frequencies for the PCL that wasused during MEW processing. In the linear viscoelastic region, i.e.,relatively small strains and strain rates as would be encountered at therelatively low flow rate conditions of the melt electrospinning writingprocess (<50 μL/h), the shear viscosity of the polymer melt can beconsidered to be Newtonian (i.e., the zero-shear viscosity,η_(o)(T_(m))). Up to a shear rate of 10 s⁻¹ the shear viscosity of PCLis constant. In the linear viscoelastic region, the uniaxial extensionalviscosity of the melt, i.e., the Trouton viscosity, is equal to threetimes the Newtonian (zero-shear) viscosity, η_(o)(T_(m))η_(p)(T _(m))=3_(o)(T _(m))  (13)Substituting the Trouton viscosity into Eq. (12) yields the followingPrintability Number, N_(PR,1):

$\begin{matrix}{N_{{PR},1} = {\frac{1}{3}\frac{\gamma^{1/2}ɛ^{1/2}}{g^{1/2}\lambda\;\rho}\frac{T_{t}}{T_{C}}\frac{R_{o}}{d}\frac{V_{p}}{Q\;{\eta_{o}( T_{m} )}}}} & (14)\end{matrix}$The zero-shear viscosities obtained from the rheological data for threedifferent melting temperatures (T_(m)=70, 80, and 90° C.) are fittedusing an Arrhenius type equation in order to obtain the activationenergy of flow (ΔH/R_(ig)) (SI:K)

$\begin{matrix}{{\eta_{o}( T_{m} )} = {{\eta_{o}( T_{ref} )}{\exp\lbrack {\frac{\Delta\; H}{R_{ig}}( {\frac{1}{T_{m}} - \frac{1}{T_{ref}}} )} \rbrack}}} & (15)\end{matrix}$where ΔH is the activation energy (SI: J/mol), R_(ig) is the universalgas constant (SI: J/K mol), and T_(ref) is the reference temperature.Substituting Eq. (15) into Eq. (14) yields the following definition ofthe Printability Number, N_(PR,1):

$\begin{matrix}{N_{{PR},1} = {\frac{1}{3}\frac{\gamma^{1/2}ɛ^{1/2}}{g^{1/2}\lambda\;\rho}\frac{T_{t}}{T_{C}}\frac{R_{o}}{d}\frac{V_{p}}{Q\;{\eta_{o}( T_{ref} )}{\exp\lbrack {\frac{\Delta\; H}{R_{ig}}( {\frac{1}{T_{m}} - \frac{1}{T_{ref}}} )} \rbrack}}}} & (16)\end{matrix}$

TABLE 4 Material properties of PCL used Parameters Values Zero shearrate viscosity (at 78° C.) (η_(o)) 3203 Pa · s Relaxation time (λ) 0.08s Activation energy of flow (ΔH/R_(ig)) 4407.8K Density of PCL (at 25°C.) 1145 kg/m³ Surface tension coefficient (γ) 30 mN/m Relativepermittivity (ε_(r) = ε/ε_(o)) 3.1

N_(PR,1) can be computed using Eq. (16) for the melting range of PCL(70° C.≤T_(m)≤90° C.) and a prescribed set of typical process andmaterial parameters. The values of the material parameters (summarizedin Table 4) are either derived from literature or through fitting of therheological data of the PCL used in processing for scaffold fabrication.In order to assure that NPR assumes values within a valid domain, eachrange is determined based on previously reported studies where PCL hasbeen successfully processed by way of MEW. Validation of the previouslyreported ranges is performed through preliminary experiments with thepresent MEW system. Thus, a range of volumetric flow rates (25 μL/h≤Q≤50μL/h) is applied for a 21 gauge needle tip diameter (D_(t)=2·R_(o)), forcollector distances (d) of 10 mm to 30 mm and a range of applied voltagepotentials (10 kV≤V_(p)≤15 kV).

The normalized N_(PR,1) is obtained by dividing the computed N_(PR,1)value with the N_(PR,1) value that defines the lower end of theprintability window bounded by the material's melting range forT_(ref)=70° C. and Q_(max)=50 μL/h. The temperature of the polymer meltinside the reservoir (T_(o)) is normalized with respect to the referencetemperature (T_(ref)=70° C.), i.e., T*=T_(o)/T_(ref). T*=T_(m)/T_(ref)since T_(o) assumes the melt temperature value (T_(m)). The printabilitywindow is seen to depend significantly on the volumetric flow rate, withthe smaller Q (25 μL/h) yielding significantly larger N*_(PR,1) valuescompared to that obtained at the larger Q (50 μL/h). This trend isconsistent with recent phenomenological observations that reflect stableprinting by way of MEW under low volumetric flow rates. As T* increaseswithin each printability window, N*_(PR,1) increases exponentially dueto the Arrhenius temperature dependence of the polymer melt viscosity,implying that for higher melt temperature conditions, the material canbe electrospun more efficiently. This relationship indicates that forprescribed D_(t), Q, and V_(p) settings, melt temperature conditionsapproaching the higher end of the material's melting temperature range(90° C. for PCL) enable earlier droplet emergence compared to the melttemperature conditions that approach the lower end of the material'smelting temperature range, due to an increased volumetric flow rateinside the needle tip.

The N_(PR,1) formulation (Eq. (16)) implies that the electrical fieldstrength (V_(p)/d) and the volumetric flow rate (Q) are the keyindependent parameters toward efficient printability (fiber meshprinting with consistent dimensional characteristics) provided that themelting and ambient conditions in the polymer melt supply regime and thetemperature profile along the spinline in the free-flow regime are notsignificantly perturbed during each printing event. N_(PR,1) scales asN_(PR,1)˜1/Q and N_(PR,1)˜V_(p)/d. This validates the physicalsignificance of the derived number that expresses the key combinatorialrole of electrostatic, viscous, and inertial forces toward steadyelectrospinning conditions as previously demonstrated for solution-basedelectrospinning systems. Furthermore, all of the dimensionless groupsare a function of Q-dependent inertial terms (see Table 3). Thus, thefunctional relationship between N_(PR,1) and each dimensionless numberis computed for the prescribed Q range and three different V_(p) valuesspanning the V_(p) range. The results are plotted for N*_(PR,1) as afunction of the Re, Ca, De, and E_(p) numbers revealing that uponprescribing the melting conditions, a unique printability window can bedefined for each V_(p) setting.

The printability window defined by the V_(p) range and the Q rangeremains to be optimized with respect to efficient printability throughin situ process monitoring and morphological characterization of theprinted meshes as described below via the experimentally collected data.

During the experimental procedure, the temperature at the surface of theglass syringe (T_(s)) is set to 78° C. The values for the remainingindependent process parameters used for the N_(PR,1) computation are setto the following for the initiation of the melt electrospinning process:(a) Q is equal to 50 μL/h, (b) V_(p) is equal to 12.5 kV, and (c) d isequal to 20 mm.

To enable real-time monitoring of the process in the free-flow regime, auniversal serial bus microscope camera is mounted on the open side ofthe enclosure box and focused on the needle tip. For this procedure, theprescribed experimental conditions reside within the printability windowcorresponding to a N*_(PR,1) equal to 1.34. The observation of theprocess during its early stages contributes to an understanding of thedynamics and the underlying physical mechanisms governing the process,as described below.

Initially, the polymer melt enters the free-flow regime owing to theelectrostatic volume forces developed from the applied voltage potentialat the tip and the mechanical force applied by the syringe pump(proportional to the pressure drop of the melt through the needle).After approximately 12 min, the jet is observed to exhibit an elongatedshape, indicating that the downstream electrostatic forces along withthe gravitational forces are sufficiently large to overcome the upstreamresistive forces (viscous, elastic, and surface tension forces). At thepoint where the downstream forces overcome the upstream resistiveforces, the formation of the Taylor cone is observed withinapproximately an additional 3 min. Immediately following the formationof the Taylor cone, a jet emerges and is electrostatically drawn betweenthe needle tip and the collector.

By extending the time course for process monitoring in the free-flowregime, it is observed that for the initially prescribed combination ofprocess parameters, excess material is generated due to the imbalancebetween the downstream pulling and upstream resistive forces. Suchexcess material that is not fully stretched periodically disturbs (every5 min) the flow field in the spinline regime. After the excess materialenters the free-flow regime, the cone shape is initially transformedinto an oblique shape, and the partially stretched melt driven by thedownstream forces leads to the relocation of the Taylor cone, i.e., thecone is pushed away from the tip of the needle, and a cylindrical bodyof melt occupies the distance between the tip of the needle and theTaylor cone. To achieve steady-state conditions, i.e., steady-stateformation of the Taylor cone at the tip of the needle and the emergingpolymer melt jet, the critical process parameters, V_(p) and Q, need tobe optimized. Such optimization specifies the relevant PrintabilityNumber N_(PR,1) at which efficient printability is achieved. Thisoptimization step thus aims to eliminate the perturbations observedunder nonequilibrium processing conditions. Upon optimization, anequilibrium state, i.e., state at which the downstream pulling andupstream resistive forces are balanced, is achieved.

The tuning of the critical independent parameters in order to achieveequilibrium conditions is carried out in a stepwise manner. As a firststep, the collector is moved closer to the needle tip (d=15 mm) toincrease the electrical field strength. When the tip to collectordistance d≤10 mm, arching occurs due to excess ionized air molecules anddry ambient conditions (humidity<25%). At such relatively smalldistances (d), the arching phenomenon becomes more pronounced forapplied voltages that are ≥15 kV. By reducing the distance (d), a higherelectrical field intensity facilitates stretching of the excess materialcollected at the tip. However, solely reducing the distance (d) is notsufficient to eliminate the periodic perturbations. To eliminate theperturbations and achieve equilibrium conditions, a reduction in thevolumetric flow rate (Q) is also required. This is suggested by therelative importance of the Q-dependent inertial forces with respect tothe V_(p)-dependent electrostatic forces, as guided by the N_(PR,1)formulation denoted in Eq. (16). The decrease of the volumetric flowrate to Q=25 μL/h results in the formation of a Taylor cone directlybelow the needle tip. However, chaotic jet movement occurs close to thecollector plate, and stable jet cannot be achieved. In order toeliminate the instabilities and establish equilibrium state conditions,the applied voltage potential can be decreased to 11.5 kV, yieldingstable cone-jet formation for a period of 30 min after which theprinting process could start.

The observation that the optimized Printability Number N*_(PR,1)=2.55)is smaller than the non-optimized Printability Number N*_(PR,1)=2.78)raises the question of self-consistency of the proposed PrintabilityNumber. This finite difference in magnitude is attributed to aphenomenon that has previously been observed in electrohydrodynamic(EHD) cone-jets with highly viscous conductive polymer solutions. Usingvoltage-flow rate (V_(p)−Q) operating diagrams, it has been shown thatfor a single Q value, steady cone-jets can be achieved for V_(p) valueslying within a range of 1 kV. Similarly, in the present example, Q ismaintained at 25 μL/h, and the voltage is decreased from 12.5 kV to 11.5kV. The decrement in V_(p) is aimed at eliminating the chaotic jetmovement close to the collector plate that is likely caused by repulsiveforces between the in-flight fiber and previously charged depositedmaterial on the collector rather than periodic flow disturbances thatare preliminarily eliminated. Therefore, the small difference betweenthe N*_(PR,1) values does not affect the self-consistent scale of thePrintability Number since it is related to the process physics, asprevious work has demonstrated. Thus, by tuning the N*_(PR,1) numberfrom an initial value of 1.34 to 2.55, the observed perturbations thatmay affect the downstream structural formability of the printed meshesand preclude efficient printability can be eliminated. This is validatedhereafter by reproducibly printing layered meshes of woven and nonwoventopographies at both the optimum and non-optimum printability settings.

After steady equilibrium conditions are achieved (i.e., for theoptimized N*_(PR,1)), the “square-wave” experiment can be conductedusing the translational stage speed as the main variable. The goals are:(a) to observe the different fiber patterns and diameters that can beproduced over a wide range of translational stage speeds and (b) todetermine the critical stage speed (U_(CR)), at which aligned fibers canbe deposited on the translating collector. At lower speeds (2-8 mm/s),random fiber deposition yields nonwoven structures typified byoverlapping fibers with multiple fusion points. At intermediatetranslation speeds (8-83 mm/s), repeatable coiling structures, for whichthe frequency of the overlap monotonically decreases as the stage speedincreases, are realized. When the translational stage speed reaches 83mm/s a well-aligned fiber with average diameter, D_(f)=23±1.5 μm(micrometer) could be printed on the collector. It should be noted thatthe changes in the translational stage speed affect the drawdown of thefiber, and thus the changes in the resulting pulling force have thepotential to disturb the equilibrium condition, especially atU_(T)»U_(CR). Thus, the optimization of the translational stage speedneeds to be carried out in conjunction with the optimization ofN*_(PR,1). To this end, U_(T) is incorporated as an additionalindependent parameter in the dimensional analysis, and the derived N₂term (Eq. (11)) is used as the Printability Number when the collector ismoving. The modified Printability Number is denoted as N_(PR,2), and itsfinal form is obtained by multiplying the N_(PR,1) with the Π₈ term.

$\begin{matrix}{N_{{PR},2} = {\frac{1}{3}\frac{\gamma^{1/2}ɛ^{1/2}R_{o}^{1/2}}{g\;\lambda\;\rho\; d}\frac{T_{t}}{T_{C}}\frac{V_{p}U_{T}}{{Q_{o}( T_{ref} )}{\exp\lbrack {\frac{\Delta\; H}{R_{ig}}( {\frac{1}{T_{m}} - \frac{1}{T_{ref}}} )} \rbrack}}}} & (17)\end{matrix}$

A normalized Printability Number, N*_(PR,2), is obtained by dividing thecomputed N_(PR,2) value (based on Eq. (17)) with the N_(PR,1) value(based on Eq. (16)) that defines the lower end of the printabilitywindow bounded by the material's melting range for T_(ref)=70° C. andQ_(max)=50 μL/h. The normalized Printability Number N*_(PR,2) iscomputed for each fiber pattern where optimum printability is achievedwhen U_(T) is tuned to its critical value (U_(T)=U_(CR)).

With the setup and calculations above, interwoven fiber meshes can bemade for use as biological scaffolds. Layered meshes with woven andnonwoven architectures are fabricated using various N*_(PR,2) settings.Woven meshes with “0-90 deg” and “0-45-135-90 deg” pore architecturesare fabricated using optimized and non-optimized N*_(PR,2) settings.When N*_(PR,2) is not optimized, irregular structures are observed. Thisis shown in FIG. 14, which is obtained at an N*_(PR,2)=31.9, whereU_(T)=25 mm/s<U_(CR). When N*_(PR,2) is increased to 57.63 byindependently tuning the stage speed (U_(T)=85 mm/s>U_(CR)) whileneglecting equilibrium conditions in the free-flow regime, alignedstructures with variable average fiber diameters (Df=27±14 μm) areobserved, as shown in FIG. 15. On the other hand, precise printing ofmesh architectures composed of well-aligned fibers with uniform averagediameters (Df=23 μm±3.7 μm) can be produced for an optimal PrintabilityNumber of N*_(PR,2)=106. The produced fibers at this optimalprintability setting are shown in FIGS. 16, 17, 18, 21 and 22 bearingthe hallmarks of equilibrium state conditions in tandem with appropriatetuning of U_(T) at its critical value.

To characterize the effects of the substrate geometry on cellconfinement states, in a first set of experiments, neonatal human dermalfibroblasts (NHDFs) were seeded directly on flat glass surfaces (toserve as controls) as well as on solution electrospun substrates (SES-1min in FIG. 19 and SES-3 min in FIG. 20) and the precision-stackedmicroarchitectures (MEW|0-90° in FIG. 21 and MEW|0-45° in FIG. 22). Theshapes of the fibroblasts were characterized at 24 h after seeding.

It was observed that the cells seeded directly on the flat glasssurfaces develop typical fibroblast morphologies exhibiting elongatedshapes and distinct actin-based motility structures (FIGS. 23-25).

It is observed that the cells seeded on MEW|0-90° are mainly attachedalong single fibers and at the intersection of layered fibers. In theformer case, cells adopt thin elongated shapes dictated by the curvatureof the fiber, since they “grab” the exposed areas of the fiber atdifferent planes (FIGS. 26-28). In the latter case, cells adopt uniformshapes and demonstrate spreading, the degree of which depends on thenumber of fibers at the intersection point.

Cells seeded on MEW0-45° are confined and suspended at various levelsacross the thickness of the substrate and within the porousmicroenvironments defined by layered fibers (FIGS. 29 and 30). Allimaged cells develop triangular lamellar shapes consistent with theenforcing triangular microarchitecture of the substrate. The cell shapesare characterized by relative few actin stress fibers that traverse thecytoplasm and terminate in distinct filopodia, with elongated focaladhesions, FAs, sequestered to the tips of the protrusions.

Taken together, these findings qualitatively suggest that there is atight link between the porous microarchitecture of precisely-stacked MEWfibrous substrates and the resulting cell morphologies. Differentstructures impose different cell confinement states. First, the cellularand subcellular morphological features of cells seeded on MEW substratesgive rise to different confinement states that are different withrespect to the ones observed in the unconfined cells cultured on glasscoverslips. Second, there exist important qualitative differences incell shapes and focal adhesion distributions, dependent on whetherrandomly-oriented solution electrospun mesh substrates or theprecision-stacked woven mesh substrates fabricated via the MEW processare used.

In a second set of experiments mesenchymal stem cells, MSCs, were used.It was then hypothesized that the induced distinct confinement states,would lead to differential downstream MSCs phenotypes. Specifically, thehypothesis was that the 3-D microscale fibrous substrates wouldconstitute a more physiological-relevant niche compared to theconventional 2-D glass substrate (controls substrate). The MSC phenotypeis characterized with respect to the expression of typical positive andnegative stem cell surface markers that allow for positive and negativeidentification that the MSCs have maintained or lost their “stemness,”respectively. To experimentally verify the purity of the MSC startingcell population, MSCs are cultured on the controls substrate and testedfor the complete set of the candidate positive and negative markers atDay 1 (24 hours after seeding). Indeed, it is observed that all thepositive CD markers are well expressed and the negative CD markers arenot expressed (FIGS. 31-36). In order to minimize the sample number thatneeds to be fabricated, the most and least well expressed positive andnegative marker (CD106+) was chosen for the rest of the characterizationstudies. At Day 7, MSCs cultured on the controls express both thepositive and negative marker, demonstrating that MSCs lose their“stemness” sometime within the first week of culture (FIGS. 33-38). Thisis in line with recent findings, according to which MSCs in standardmonolayer cultures loose stem cell marker expression by Day 3 ofculture.

Remarkably, it is observed that MSCs on the MEW|0-90° remain viable andself-renew by populating the effective fiber adhesive area withoutlosing their phenotype during the first week of culture (FIGS. 39-50).The time course of the experiment was extended to two weeks,demonstrating that cells continued to proliferate without losing theirstem cell marker expression (FIGS. 51-62). Then, it was tested whetheran altered porous microarchitecture under a 3-D setting could result indifferential MSCs phenotypes compared to the controls and the MEW|0-90°substrate at the prescribed time points. It is observed that MSCsmaintain their stemness during the first week of culture on MEW|0-45°substrates (FIGS. 63-70), while they lose their MSC phenotype sometimeduring the second week of culture (FIGS. 65-72).

A last set of experiments was performed to study long term (after 33days) stem cell differentiation on both flat and 3-D microscalescaffolds. The results are depicted in FIGS. 75-82, demonstratingpositive adipocyte (FIGS. 75 and 76) and bone (FIGS. 77-78)differentiation marker expression 33 days after culture on conventionalflat substrates and demonstrating in FIGS. 79 and 80 and FIGS. 81-82only adipocyte differentiation marker expression on MEW scaffolds,further illustrating the expansion of stem cells on scaffolds havingporous microarchitecture realized according to a method of the presentinvention promotes homogeneous expansion and differentiation of stemcells.

Thus, it was determined that stem cells seeded on exemplary scaffoldsfabricated by the TCK method behave in a very different manner from stemcells seeded on conventional 2-D surfaces with regard to the spatialmanner by which they adopt characteristic shapes, position themselves,and migrate with respect to time on these controlled scaffoldgeometries. Significant differences in these spatial outcomes for stemcell behavior were also observed to arise from changes in scaffoldgeometries. For example, a comparison of 0-45° versus 0-90° scaffoldconfigurations according to an embodiment of the present inventionshowed stem cell positioning, shape, and migration that differed betweenthe two scaffold geometries, demonstrating that the spatialcharacteristics of stem cells could be independently controlled solelyvia scaffold and bioreactor substrate geometries.

Embodiments of the present invention include a method for quantitativelyand reliably characterizing the measurements of cell position vectorsand cell shapes. A block diagram of the metrology method is depicted inFIG. 83. Embodiments of the characterization method enable the rapid andreliable analysis and characterization of many cells under conditions ofhigh throughput. Embodiments of the characterization method includeimmunofluorescent labeling of the cells for identification of structuraland functional features with subsequent 3-D image acquisition, whereinthe functional features include cell surface markers. Embodiments of thecharacterization method further include image analysis and automatedalgorithms for analyzing immunofluorescent-labeled cell features (FIG.84), and generating statistics for the cell position and shapedistributions that are then correlated with the stem cell phenotype.Embodiments of this method are referred to hereinafter as the “SIT”classification method. In embodiments of the present invention, the SITclassification method is integrated into an overall methodology ofdiscovering the appropriate geometries for generating desirable cellshapes and phenotypes during the expansion of seeded cells.

In an embodiment of the present invention, images of a cell weregenerated via quantitative fluorescence confocal microscopy. Sampleimages appear in FIGS. 85-88, wherein a non-segmented view of a wholecell, a segmented view of just the cell body, a segmented view of justthe nucleus body and a view displaying only the cell's focal adhesionsare shown.

In an embodiment of the current invention, a FA metrology framework thatallows the definition of metrics that model the distribution of the FAproteins at the cell level is disclosed. It can be understood asincluding three phases, as illustrated in FIG. 84.

First is the data acquisition phase, where the samples are imagesobtained with a high resolution confocal microscope equipped with 3laser lines at 63× magnification and the samples are scanned acrosstheir thickness with a 0.1 μm step size. In this way, 3 sets ofgrayscale raw images can be produced for each cell, corresponding to thecellular and sub-cellular features of interest: FAs, ActinMicrofilaments and Nuclei as depicted in FIGS. 85-88.

During the image processing phase, an algorithmic workflow where FAs canbe automatically detected and segmented in each raw grayscalefluorescent image can be used, allowing for the 3-D volumereconstruction of all of the FAs within one cell in an xyz Cartesiancoordinate system.

The image processing algorithmic procedure allows the development ofcritical cellular and subcellular focal adhesion morphometric anddistribution metrics that are useful for the training and application ofthe developed classification method to various cell types according toan embodiment of the present invention. The results are depicted inFIGS. 89-97. During the modeling phase, metrics that describe thedistribution characteristics of the proteins can be defined. The valuesof these metrics could possibly be FA-representative of the whole cellpopulation within each sample.

In an embodiment, focal adhesions can be detected and segmentedaccording to the algorithm. Initially the cell body is generated usingthresholding and filtering techniques from a raw grayscale image coloredgreen. Then, the individual FAs are detected and accurately segmentedwithin the detected region of interest. Specifically, Clahe, whichstands for “contrast limited adaptive histogram equalization,” is usedto equalize image brightness and contrast across the processed image.

In an embodiment, a thresholding step is performed, which automaticallydesignates pixels as black or white based on whether they are above orbelow a certain pixel value.

In an embodiment, a dilation step is performed, wherein white pixels areremoved if they are surrounded by a number of black pixels greater thanor equal to the specified value.

In an embodiment, an erosion step is performed, wherein black pixels areremoved in the same way as white pixels are removed in the dilationstep.

In an embodiment, a reject features step is performed in which infiniteareas corresponding to white or black pixels are removed.

In an embodiment, a Wiener filter is applied, which reduces the sparsenoise while preserving edges

In an embodiment, a fast Fourier transform is performed to reducebackground noise and artifacts.

A manual review of the algorithm's output is advisable, to verify theaccuracy of the algorithm.

Following the same image processing algorithmic workflow for not onlythe FA channel, but also for the Actin Microfilament and DAPI channelallows for the 3-D volume reconstruction of each feature. They can thenbe merged into a composite image for visual inspection.

Two metrics were developed for the SIT algorithm. In particular, theradial Euclidean distances between focal adhesion and nuclei centroidswere recorded for both a 2-D petri dish control and a 3-D confined andsuspended state (i.e., 0-45° scaffold) system. Frequency distributionmodeling was performed based on the Euclidean distance. A function wasdeveloped to characterize the relationship between radial Euclideandistances and the frequency of FAs within such a distance. From thisE-function the slope was taken as the E-slope parameter. An increase inthis E-slope parameter correlates with the formation of more FAs closerto the nucleus.

A similar frequency distribution modeling was also performed with thedistance from each focal adhesion to its closest neighbor. A G-functionwas generated based on the relationship between nearest neighbordistance and the frequency of focal adhesions in this range. A smallerG-function value correlates with a more aggregated FA pattern at theindividual/single cell level.

A morphometric analysis found that FA number and total area of FAs werenot statistically significant when comparing melt electrospinningwriting scaffolds with conventional controls (i.e., randomly electrospunmeshes and a glass medium). However, FA size was higher for the MEWscaffold. Additionally the aspect ratio of the FAs in this experimentcorrelated with the ellipticity of the cell shape.

It was also found that cell area had no statistical differences betweenthe four conditions, though the random fibrous substrates did havegreater solidity. This is believed to be due to these fibers introducingrandom candidate cell attachment, resulting in more ruffled cell-shapes.Meanwhile 0-45° MEW-printed scaffolds saw triangular cell shapes withdistinct cell attachment points. Thus, the MEW embodiment saw lowerrectangularity and ellipticity.

A 7-D Cartesian coordinate system of cell shape phenotypes, in whicheach axis represents a feature metric, was developed for the 7 metricscomputed from the Morphometric described above. a) Global (over apopulation of cells) E-slope (“I”), b) Rectangularity (“II”), c) Global(over a population of cells) mean G-function (“III”), d) FA size (“IV”),e) FA Aspect Ratio (“V”), f) Ellipticity (“VI”), g) Cell Area (“VII”)were chosen as the seven, dimensional parameters. Within thisrepresentation, each point represents one single cell feature-vectorwith 7 elements corresponding to the computed metrics for the specificcell. All metrics are normalized using a Z-score function, which centersand scales all metric values to have zero mean and unit standarddeviation, respectively. The transformed metric vectors for each cellpopulation are multidimensional datasets to train a Support VectorMachine (SVM) with a linear kernel using the classification learnerpackage in MATLAB. The linear-kernel SVM is a supervised machinelearning algorithm that can classify the data by finding the besthyperplane that separates all data points into: a) a class representingcells being in a 2-D unconfined state (Class A) and b) a classrepresenting cells being in a 3-D confined state (class D). The besthyperplane for the SVM algorithm is considered the one with the largestmargin between the two classes with the margin being the maximum widthof the slab parallel to the hyperplane that has no interior data points.The predictive accuracy of the linear-kernel SVM can be assessed using a5-fold cross-validation scheme to protect against overfitting. Here, thedata are randomly partitioned in 5 folds where, for each fold, thescheme trains the linear SVM using the out-of-fold observations andassesses the model performance using the in-fold data. Theclassification accuracy is defined as the average percentage of thecorrectly classified data for each fold and used as a metric for theclassifier's predictive performance.

The results of the machine learning task, which is the classification ofcell shape phenotypes modeled for every scaffold are depicted in FIGS.98-103. While the initial assessment of the discriminatory informationof each metric provides valuable insights concerning the cell shapephenotypic differences across and within each cell population group, theability to infer the substrate dimensionality and architecture directlyfrom single cell morphologies remains to be validated. To accomplishthat, the single-cell multi-dimensional data sets are used to train thechosen machine learning algorithm with the aim of distinguishing betweenfour different classes by considering all features simultaneously. Theclass declaration is depicted in Table 5 below, where all substratedimensionalities and topographies are depicted along with the cellconfinement states:

TABLE 5 Substrate Cell Dimensionality - Architecture Confinement StateClass (METROLOGY- FIGS. 12 AND 13) (OBSERVATIONS) A 2-D uniformunconfined (Controls - Glass surfaces) B random confined (SES - 1 min) Crandom confined (SES - 3 min) D 3-D uniform confined (MEW | 0-45°)

Three different classification tasks are performed. Combinations of thescaled metrics are plotted to allow easier assessment of the results(FIGS. 98-103). The capability of the classifier to operatesatisfactorily with data outside the training set for eachclassification task is assessed based on the classification accuracy.Initially, the multi-class classification problem is attempted by takinginto account cell morphologies across all the fabricated substrates(FIGS. 100 and 101). The classifier demonstrates a low classificationaccuracy (67%), which can be explained by the large intra-class varianceof Class B. By removing Class B, the classification accuracy increasesto 90.6%, demonstrating that the trained classifier can predict withhigh accuracy the substrate from which a cell originates based strictlyon its feature vector identity. Remarkably, when the binaryclassification task is run by combining all classes corresponding to theflat or electrospun SES substrates, including the “noisy” Class Bagainst Class D, the classification accuracy level remains around 93%.Thus, it is demonstrated that the 3-D microscale precision-stackedsubstrates promote a confined and suspended state that morphologicallystands out both at the cellular as well as the sub-cellular FA level.

It is concluded that the MEW substrates may promote less migratory earlycell shape phenotypic responses that are characteristic of a confinedand suspended state. These responses are distinct from the confinementstates adopted by the more actively motile cells on the flat andelectrospun SES substrates. In the former case, cells tend to develop amore aggregated pattern of larger and less elongated mature FAs withincell bodies. The global shapes of the cells are dictated by thesubstrate's triangular porous microarchitecture. In the latter case,cells tend to develop a more dispersed pattern of mature FAs within moreelliptic cell bodies. Across the 2-D substrates, the degree of theresultant cell confinement appears to be regulated by the extent offiber coverage with the cells on the controls substrate (0% of fibercoverage) being in an unconfined state. Lastly, the substrates'structural heterogeneity with respect to fiber diameter and pore sizedistribution dictates the variance of the defined morphometric andprotein distribution metrics with the MEW|0-45° and SES-3 min substratedemonstrating the most and least homogeneous population of single cellmorphologies, respectively.

Integration of embodiments of the TCK fabrication method and embodimentsof the SIT classification scheme enable discovery of the extent and timeduration over which stem cells conserve their shapes and phenotypes,thereby facilitating manipulation of the shapes and phenotypes of thestem cells using the geometry of the scaffold or the bioreactorsubstrate as a tool. A schematic diagram of a concept for industrialexploitation of the classification method according to an embodiment ofthe present invention, further including feedback and feedforwardcontrol methodologies for the programmable expansion and harvesting ofstem cells having phenotypes that are targeted and realized according toa method of the present invention is depicted in FIG. 104. By suchmeans, stem cell therapies can be improved significantly by tailoringthe geometries of scaffolds and bioreactors used during theadministration of such therapies.

It will be understood that the embodiments described herein are merelyexemplary and that a person of ordinary skill in the art may make manyvariations and modifications without departing from the spirit and scopeof the invention. All such variations and modifications are intended tobe included within the scope of the invention as disclosed, includingany and all such variations and modifications disclosed in MeltElectrospinning Writing Process Guided by a “Printability Number,”published in the Journal of Manufacturing Science and Engineering,August 2017, Vol. 139, pgs. 081004-1 to 081004-15, the contents of whichare incorporated herein in their entireties.

We claim:
 1. A three-dimensional scaffold, comprising a poroustriangular microarchitecture having a 0-90 degree or 0-45 degree porestructure provided by a plurality of woven porous substrates stacked oneach other, the porous microarchitecture having geometrical featuresizes of about 100 microns or smaller, and each of the woven poroussubstrates comprising a plurality of polycaprolactone fibers that areinterwoven together.
 2. The three-dimensional scaffold of claim 1, theporous triangular microarchitecture comprising a plurality of triangularpores that are substantially uniform in size and shape.
 3. Thethree-dimensional scaffold of claim 1, the plurality of woven poroussubstrates being fabricated from a polycaprolactone melt using a meltelectrowriting technique.
 4. The three-dimensional scaffold of claim 1,the plurality of woven porous substrates being fabricated by meltelectrowriting.
 5. The three-dimensional scaffold of claim 1, thegeometrical feature sizes being 10-100 μm.
 6. The three-dimensionalscaffold of claim 1, the plurality of fibers having a submicrondiameter.
 7. The three-dimensional scaffold of claim 1, the porousmicroarchitecture having a 0-45-135-90 degree pore structure.
 8. Amethod of expanding cells in vitro, comprising: providing thethree-dimensional scaffold of claim 1, seeding a plurality of cells onthe three-dimensional scaffold, culturing the cells to obtain expandedcells that are substantially uniform in shape and phenotype.
 9. Themethod of claim 8, wherein the cells are stem cells and the expandedcells maintain stemness.
 10. The method of claim 8, wherein the expandedcells are homogenous.
 11. The method of claim 8, further comprisingdetermining a relationship between the porous microarchitecture and theshape and phenotype of the expanded cells.
 12. The method of claim 8,further comprising generating a metrology framework that models andclassifies cell confinement states for various porousmicroarchitectures.
 13. The method of claim 8, further comprisingclassifying cell shapes and/or focal adhesions using machine learning.14. The method of claim 13, wherein the machine learning is carried outusing immunofluorescent imaging of the expanded cells.
 15. The method ofclaim 13, wherein the immunofluorescent imaging comprisesimmunofluorescent labeling of positive and/or negative cell surfacemarkers.
 16. The method of claim 8, further comprising tuning so as toreproducibly harvesting targeted cell populations.